Answer:
The standard from of the expression is: [tex](x +1)^2 + (y-1)^2 = (2)^2[/tex]
Step-by-step explanation:
Here the given expression is :
[tex]x^2+2x+y^2-2y=2[/tex]
Now, the standard form of a circle is given as :
[tex](x-h)^2 + (y -k)^2 = r^2[/tex]
Here, (h,k) = Coordinates of Center, r = Radius
Also, use the algebraic identity:
[tex](a \pm b)^2 = a^2 + b^2 \pm 2ab\\[/tex]
Now, converting the given expression in the standard form, we get:
[tex]x^2+2x+y^2-2y=2[/tex]
Add 2 on both sides of the equation, we get:
[tex]x^2+2x+y^2-2y +2=2 + 2\\\implies x^2+2x + 1 + y^2-2y + 1 = 4\\\implies (x^2+2x + 1 )+ (y^2-2y + 1) = 4\\\implies (x +1)^2 + (y-1)^2 = (2)^2[/tex]
So, here the standard from of the expression is:
[tex](x +1)^2 + (y-1)^2 = (2)^2[/tex]
Center coordinates here are (h,k) = ( -1 ,1) and Radius = 2 units
Please help me the brainliest.
Answer:
A² - B² = 0 (Proved).
Step-by-step explanation:
Given that
[tex]A = \frac{\cot \theta + \csc \theta - 1}{\cot \theta - \csc \theta + 1}[/tex]
⇒[tex]A = \frac{\csc \theta + \cot \theta - (\csc^{2} \theta - \cot^{2} \theta)}{\cot \theta - \csc \theta + 1}[/tex]
{Since, we know the identity as [tex]1 = \csc^{2} \theta - \cot^{2} \theta[/tex]}
⇒ [tex]A = \frac{\csc \theta + \cot \theta - (\csc \theta + \cot \theta)\times (\csc \theta - \cot \theta)}{\cot \theta - \csc \theta + 1}[/tex]
⇒ [tex]A = \frac{(\csc \theta + \cot \theta) (\cot \theta - \csc \theta + 1)}{\cot \theta - \csc \theta + 1}[/tex]
⇒ [tex]A = \csc \theta + \cot \theta[/tex]
Again, given that [tex]B = \csc \theta + \cot \theta[/tex]
So, A = B . ⇒ (A - B) = 0.
Hence, A² - B² = (A + B)(A - B) = 0 (Proved)
A dairy needs 332 gallons of milk containing 6% butterfat. How many gallons each of milk containing 7% butterfat and milk containing 3% butterfat must be used to obtain the desired 332 gallons?
Answer:
249 gallons of 7% butterfat milk and 83 gallons of 3% butterfat milk
Step-by-step explanation:
If x is the gallons of 7% butterfat milk, and y is the gallons of 3% butterfat milk, then:
x + y = 332
0.07x + 0.03y = 0.06(332)
Solve the system of equations using substitution:
0.07x + 0.03(332 − x) = 0.06(332)
0.07x + 9.96 − 0.03x = 19.92
0.04x = 9.96
x = 249
y = 332 − x
y = 83
You need 249 gallons of 7% butterfat milk and 83 gallons of 3% butterfat milk.
What is Y/2 +3.2=5.06
Answer:
y=3.72
Step-by-step explanation:
y/2+3.2=5.06
y/2=5.06-3.2
y/2=1.86
y=1.86*2
y=3.72
Answer:
y= 3.72
Step-by-step explanation:
reverse the operations
5.06-3.2= 1.86
1.86*2= 3.72
y=3.72
a rectangles width is 4 less than its area and its length is 19. what is it’s width?
The width of the rectangle is [tex]\frac{2}{9}[/tex] unit
Step-by-step explanation:
The given is:
A rectangles width is 4 less than its areaIts length is 19 unitsWe need to find the width of the rectangle
Assume that the width of the rectangle is x units
∵ The area of the rectangle = length × width
∵ The width of the rectangle = x units
∵ The length of the rectangle = 19 units
∴ The area of the square = 19 × x = 19 x units²
∵ The width of the rectangle is 4 less than its area
- That means subtract 4 from the area to find the width
∴ x = 19 x - 4
- Subtract 19 x from both sides
∴ -18 x = -4
- Divide both sides by -18
∴ x = [tex]\frac{-4}{-18}[/tex]
- Reduce the fraction by dividing up and down by -2
∴ x = [tex]\frac{2}{9}[/tex]
The width of the rectangle is [tex]\frac{2}{9}[/tex] unit
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The student setup 30 games booths;the teachers also setup some. If 5/6 of the game booths were set up by the students, how many game booths are there in total?
The total number of game booths is 36, with the students setting up 30 booths denoting 5/6 of the total, and teachers setting up the remaining 6 booths which corresponds to 1/6 of the total.
Explanation:The student question asks about finding the total number of game booths if 5/6 of them were set up by students, and it is known that students set up 30 booths. First, we assume the fraction 5/6 represents the portion of booths that the students were responsible for setting up. Since 5/6 equates to the 30 booths the students set up, each fraction of 1/6 represents 6 booths (30 divided by 5). As there are 6 fractions of 1/6 in a whole, to find the total (which is 6/6), you simply multiply 6 (the value of 1/6) by 6.
The calculation is as follows: 6 booths per 1/6 x 6 = 36 game booths in total. Therefore, the teachers set up the remaining sixth, which corresponds to 6 game booths, making the combined total 36. This result indicates that there is a total of 36 game booths when we include the contributions from both students and teachers.
In this case, There are 36 game booths in total.
Let's denote the total number of game booths as T.
According to the information given, 5/6 of the game booths were set up by the students.
Since the students set up 30 game booths, we can write the following equation:
[tex]\[\frac{5}{6}T = 30\][/tex]
To find the total number of game booths, T, we need to solve for T.
We can do this by multiplying both sides of the equation by the reciprocal of 5/6, which is 6/5:
[tex]\[T = 30 \times \frac{6}{5}\][/tex]
Now, we calculate the value of T:
[tex]\[T = 30 \times \frac{6}{5}\][/tex]
T = 36
Therefore, there are 36 game booths in total.
The three-dimensional figure below is a solid rectangular prism with a hole in the shape of another rectangular prism going through the center of it. Find the volume of the solid in cubic centimeters.
A solid rectangular prism with a hole in the shape of another rectangular prism going through the center of it is shown. The rectangular prism is 20 centimeters long, 5 centimeters wide, and 5 centimeters high. The rectangular prism-shaped-hole is 20 centimeters long, 2 centimeters wide, and 2 centimeters high.
The volume of the solid is 420 cm³
Step-by-step explanation:
The volume a rectangular prism is calculated as the product of its length, width and height.
Mathematically, V=l*w*h where l is length of the prism, w is width and h is the height
Given that the dimensions of the rectangular prism as;
Length=20 cm
Width= 5 cm
Height = 5 cm
V=20*5*5= 500 cm³
The rectangular prism shaped hole dimensions are;
Length= 20 cm
width= 2 cm
Height= 2 cm
Volume= 20*2*2=80 cm³
The volume of the solid will be: volume of rectangular prism-volume of the hole
Volume= 500-80=420 cm³
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The volume of the solid rectangular prism with a hole is 420 cm³.
To find the volume of the solid rectangular prism with a hole, we follow these steps:
Volume of the Outer Rectangular Prism:
Using the formula V = l * w * h, where l is the length, w is the width, and h is the height of the outer rectangular prism:
Volume of the outer prism (V_outer) = 20 cm * 5 cm * 5 cm = 500 cm³.
Volume of the Rectangular Prism-shaped Hole:
Using the same formula for the inner rectangular prism:
Volume of the hole (V_hole) = 20 cm * 2 cm * 2 cm = 80 cm³.
Volume of the Solid:
Subtracting the volume of the hole from the volume of the outer prism:
Volume of the solid (V_solid) = V_outer - V_hole = 500 cm³ - 80 cm³ = 420 cm³.
Therefore, the volume of the solid rectangular prism with a hole is 420 cm³.
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Solve for k 1/4 k=3(-1/4K+3)
Answer:
k=9
Step-by-step explanation:
1/4k=3(-1/4k+3)
1/4k=-3/4k+9
1/4k-(-3/4k)=9
1/4k+3/4k=9
k=9
Step by step I need
The circumference of a circle with a 6 in diameter using pi
[tex]\bf \textit{circumference of a circle}\\\\ C=\pi d~~ \begin{cases} d=diameter\\[-0.5em] \hrulefill\\ d = 6 \end{cases}\implies C=6\pi \implies C\approx 18.85[/tex]
For a certain value of k, the system
[tex]x+y+3z=10,\\
-4x+2y+5z+7,\\
kx+z=3,[/tex]
has no solutions. What is the value of k?
The value of k that makes the system of equations have no solution is k = -0.25. This is because -0.25 makes the third equation parallel to the first two, resulting in no intersection or solution to the system.
Explanation:The system of equations provided relates to the concept of systems of linear equations in mathematics. When a system of equations has no solution, it means the graphs of the equations do not intersect. To find the value of k where there is no solution, we determine when the planar coefficients of each equation are proportional. This occurs when the two planes are parallel and hence, do not intersect.
By examining the coefficients, we notice that dividing the coefficients from the first equation by -4 gives us the coefficients of the second equation, meaning the first two equations represent the same plane. Thus, k does not affect the first two equations. For the system to have no solutions, the third plane must be parallel to the first two, meaning the coefficients must have a ratio equal to k. If we set the coefficients from the third equation with the coefficients from the first one, we end with the proportion k/1 = 1/-4 = 3/10. Solving for k gives us a value of -0.25.
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Which of the following point-slope form equations could be produced with the points (2, -6) and (4, -3)?
y - 6 = 3/2(x + 2)
y - 6 = 3/2(x - 2)
y + 6 = 3/2(x - 2)
y + 6 = -3/2(x + 2)
Answer:
y+6=[tex]\frac{\textbf{3}}{\textbf{2}}[/tex](x-2)Step-by-step explanation:
A line passes through the points [tex](2,-6)[/tex] and [tex](4,-3)[/tex].
To find the point-slope form of the line, we need a point on the line and the slope of the line.
As we have two points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex], the slope can be calculated as [tex]\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].
Slope of the line = [tex]\dfrac{-3-(-6)}{4-2}=\dfrac{3}{2}[/tex]
Given a line with slope [tex]m[/tex] and a point [tex](x_{1},y_{1})[/tex], slope-point form is [tex]y-y_{1}=m(x-x_{1})[/tex]
Line is given by [tex]y+6=\frac{3}{2}(x-2)[/tex]
∴ The line is given by [tex]y+6=\frac{3}{2}(x-2)[/tex]
Final answer:
The correct point-slope form equation with the points (2, -6) and (4, -3) is y + 6 = 3/2(x - 2), after finding the slope of 3/2 and applying it to the point-slope formula using either of the points.
Explanation:
Firstly, let's find the slope of the line passing through the points (2, -6) and (4, -3). The slope formula is
(y₂ - y₁) / (x₂ - x₁), so plug in the values to get (-3 - (-6)) / (4 - 2) = 3 / 2.
Now we know the slope is 3/2, we can write a point-slope form equation, which is y - y₁ = m(x - x₁). We can use either of the given points; let's use (2, -6). Substituting these values into the point-slope formula gives us: y - (-6) = 3/2(x - 2).
Thus, the correct point-slope form equation produced with the points (2, -6) and (4, -3) is: y + 6 = 3/2(x - 2).
the dimensions of a blackboard are 9/10 of a meter by 7/10 of a meter. In drawing of the blackboard given below, 1/2 of a inch represents 2 meters. What is unit rate of area in square meters of the blackboard per square inch of area in the drawing?
Answer:
16 square meters per square inch
Step-by-step explanation:
we know that
The scale drawing is
[tex]\frac{(1/2)}{2}=\frac{1}{4}\ \frac{in}{m}[/tex]
That means ---> 1 in in the drawing represent 4 meters in the actual
Find the dimensions of the blackboard in the drawing
Divide by 4
[tex]\frac{9}{10}\ m=\frac{9}{10}/4=\frac{9}{40}\ in[/tex]
[tex]\frac{7}{10}\ m=\frac{7}{10}/4=\frac{7}{40}\ in[/tex]
Find the area of the blackboard
[tex](\frac{9}{10})(\frac{7}{10})=\frac{63}{100}\ m^2[/tex]
Find the area in the drawing
[tex](\frac{9}{40})(\frac{7}{40})=\frac{63}{1,600}\ in^2[/tex]
Find out the unit rate of area in square meters of the blackboard per square inch of area in the drawing
[tex](\frac{63}{100})/(\frac{63}{1,600})=\frac{1,600}{100}=16\ \frac{m^2}{in^2} [/tex]
23,478 round to the nearest ten thousands
Rounding to the nearest ten thousands, look at the thousands number, if it is 5 or higher round up, if it is less than 5 round down.
The thousands number is 3, so round down to the neareast ten thousands:
The answer would be 20,000
The number 23,478 rounded to the nearest ten thousands is 20,000
How to determine 23,478 to the nearest ten thousandsFrom the question, we have the following parameters that can be used in our computation:
Number = 23,478
By definition, to round a number to the nearest nearest ten thousands, look at the next place value to the right (the hundred thousands)
Using the above as a guide, we have the following:
Number = 20,000 to to the nearest ten thousands
Hence, the number to to the nearest ten thousands is 20,000
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14. Luis placed $4500 in a certificate of deposit. He earns $20 each month
for the next 36 months. Find the annual simple interest rate for the
certificate of deposit.
To find the annual simple interest rate for the certificate of deposit, divide the total interest earned by the principal amount. In this case, the annual interest rate is 16%.
Explanation:The amount of simple interest Luis earns each month is $20, and he earns this for the next 36 months. We can find the total interest earned by multiplying the monthly interest by the number of months: $20 x 36 = $720.
To find the annual simple interest rate for the certificate of deposit, we need to divide the total interest earned by the principal amount. In this case, the principal amount is $4500. So, the annual interest rate is calculated as: $720 / $4500 = 0.16 or 16%.
Therefore, the annual simple interest rate for the certificate of deposit is 16%.
What is another way to write 75 ?
5×5×5×5×5×5×5
7+7+7+7+7
7×7×7×7×7
5+5+5+5+5+5+5
Answer:
All Of these Answer are INCORRECT!
Step-by-step explanation:
You Can tell by the first three fives in the first answer..
5*5=25*5=125=NOT GONNA WORK!
7+7+7+7+7=35= NOT GONNA WORK!
7x7 wont make it= NOT GONNA WORK!
There Never Gonna Work!
The factors of a number is are those which produce the same number when two numbers are multiplied together. It can be written as 3 × 5² or also as 15 × 5 and also as 1 × 75. The given options are not correct.
What are factors of 75?The factors of 75 are defined as the numbers which are multiplied in pairs resulting in the original number 75. In other words, the factors of 75 are also the numbers which divide the number 75 exactly without leaving the remainder.
Here 75 is a composite number and it has many factors other than the number itself. The factors of 75 are 1, 3, 5, 15, 25 and 75. In order to obtain a pair factor, multiply the two numbers in a pair to get the original number.
The pair factors of 75 are:
3 × 25 = 75
5 × 15 = 75
25 × 3 = 75
15 × 5 = 75
So the given options are not correct.
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The difference between two numbers is 78. Five times the smaller is equal to 6 more than the larger. What are the numbers?
10. Write an equation in point-slope form and slope-intercept form for the line.
Passes through (2,-2) and (4,-1)
We can use the points (2, -2) and (4, -1) to solve.
Slope formula: y2-y1/x2-x1
= -1-2/4-(-2)
= -3/6
= -1/2
Point slope form: y - y1 = m(x - x1)
y - 2 = -1/2(x + 2)
Solve for y-intercept.
-2 = -1/2(2) + b
-2 = -1 + b
-2 + 1 = -1 + 1 + b
-1 = b
Slope Intercept Form: y = mx + b
y = -1/2x - 1
______
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Solve for m. 12m-15=3(2m+3)
Answer:
m = 4
Step-by-step explanation:
12m - 15 = 3 (2m + 3)
12 m - 15 = 6m + 9
12m - 6m - 15 = 6m - 6m + 9
6m - 15 = 9
6m - 15 + 15 = 9 + 15
6m = 24
(1/6) 6m = 24 (1/6)
m = 4
Height is proportional to foot length. A person whose foot length is 10 inches is 67 inches tall. A human-like creature has a foot length of 35 inches. Use a proportion to find the height of the creature.
Answer:
the creature 268 inches tall
Step-by-step explanation:
set it up and cross multiply!
10 = 40
67 X
67*40=10*X
2680=10X
then divide 10 from both sides:
so X=268
solve 2cos^2x+sinx-1=0, if 0<=x<=2pi
The equation 2cos²x + sinx - 1 = 0 can be solved by converting terms involving cosine to sine, simplifying the equation, and then solving the resulting quadratic equation for sinx and consequently solving for x.
Explanation:To solve the trigonometric equation 2cos²x + sinx - 1 = 0, we can first convert the terms in the equation involving cosine to terms involving sine.
We know that cos²x= 1 - sin²x. Substituting this into the equation, we will have 2(1 - sin^2x) + sinx - 1 = 0.
This simplifies to 2 - 2sin²x + sinx - 1 = 0. Reordering terms, we get 2sin²x - sinx + 1 = 0. If we solve this quadratic equation for sinx, we can then solve for x. Assuming the domain 0<=x<=2pi, this will give us the possible values of x that satisfy the original equation.
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Place the indicated product in the proper location on the grid.
(4ya - 6xb)(4ya + 6xb)
Answer:
Simplify the expression.
16y^2a - 36x^2b
Step-by-step explanation: hope this helps!
Two quantities are related, as shown in the table:
x y
2 3
4 4
6 5
8 6
Which equation best represents the relationship?
y = 1 over 2 x + 2
y = 1 over 2 x + 1
y = x + 2
y = 2x + 1
Answer:
[tex]y = \frac{1}{2} x + 2[/tex].
Step-by-step explanation:
From the given table it is clear that x and y are linearly related.
Now, any two points that satisfy the relation between x and y are sufficient to express the equation.
The first two given points are (2,3), and (4,4).
Therefore, the equation is [tex]\frac{y - 4}{4 - 3} = \frac{x - 4}{4 - 2}[/tex]
⇒ [tex]y - 4 = \frac{1}{2} (x - 4)[/tex]
⇒ [tex]y - 4 = \frac{1}{2} x - 2[/tex]
⇒ [tex]y = \frac{1}{2} x + 2[/tex]. (Answer)
Answer:
A
Step-by-step explanation:
bc i said so
Please help quickly!
Answer:
times it by 3 on both sides should get 180
Step-by-step explanation:
Rosa brought d drawings to an art show. After selling 15 of them, she had 38 left. Identify the equation that represents the situation and the correct solution.
The Answer:
D
Step-by-step explanation:
d=53
The next model of a sports car will cost more than the current model. The current model costs . How much will the price increase in dollars? What will be the price of the next model?
Answer:
$1677
$40677
Step-by-step explanation:
Compared to the price of the current model sports can the next model price will be 4.3% higher.
The cost of the current model sports car is $39000.
Therefore, the price will increase in the next model by [tex]\frac{39000 \times 4.3}{100} = 1677[/tex] dollars. (Answer)
Now, the price of the next model will be $(39000 + 1677) = $40677 (Answer)
The price increase in dollars for the next sports car model, priced at 4.3% more than the current value, is $1,677. So, the next model of the sports car will cost $40,677.
Explanation:The subject of this question is about the calculation of a price increase in mathematical terms. If the next model of a sports car is going to cost 4.3% more than the current model, which costs $39,000, then first we need to find out how much exactly 4.3% of $39,000 is. The calculation involves multiplying 39,000 by 4.3%, which comes out to $1,677.
Therefore, the price of the next model of a sports car will be the current price which is $39,000 plus the price increase in dollars i.e., $1,677. Hence, adding the two amounts gives us a total cost of $40,677 which is the price of the upcoming model.
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What shape best describes the cross section cut at an angle to the base of a right rectangular prism? Trapezoid Parallelogram Square Rectangle
HURRY URGENT
Answer:
Parallelogram
Step-by-step explanation:
dis
You roll a fair 6-sided die.
What is P(not 5)?
If necessary, round your answer to 2 decimal places.
ro
Answer:
There would be an 83.3% chance (0.83 chance) that the die would not land on 5.
Step-by-step explanation:
Use the probability formula: [tex]\frac{desired}{total}[/tex] (desired events over total events)
There are 5 desired events. (The events that the die would not land on five)There are 6 total events.[tex]\frac{desired}{total} =\frac{5}{6}= 0.8333333[/tex]
Rounded to two decimal places, there would be a 0.83 chance that the die would not land on 5.
Determine algebraically whether the function is even, odd, or neither even nor odd. f(x) = x + 4/x
Answer:
The given function is an odd function.
Step-by-step explanation:
We define a function f(x) as even function when f(-x) = f(x) and odd function when f(-x) = - f(x) and otherwise it is neither even nor odd function.
Now, we are given a function of x as [tex]f(x) = x + \frac{4}{x}[/tex] and we have to deternime whether the function f(x) is even, odd, or neither even nor odd.
Now, [tex]f(-x) = - x + \frac{4}{- x} = - x - \frac{4}{x} = - [x + \frac{4}{x}] = - f(x)[/tex]
Therefore, the given function is an odd function. (Answer)
Two skaters are racing towards the finish line of the race.the first Skater has a 40 meter lead and is traveling at a rate of 12 meter.the second skater is traveling at a rate of 14 meter per second.how long will it take for the second skater to pass the first skater?
Answer:
20 seconds
Step-by-step explanation:
The distance to cover between the lead skater and trailing skater is 40 meters
The lead skater's rate is 12 m/s
The trailing one's rate is 14 m/s
So, we can say:
second skater is accelerating, or covering up the distance, in 14 - 12 = 2 m/s
So, at a rate of 2 meters per second, how long would it take to cover 40 meters??
We use the distance formula, substitute the known and solve for unknown.
Distance Formula = D = RT
Where
D is distance
R is speed/rate
T is time
We know
r = 2 m/s
d = 40 m
t = ?
Now,
D = RT
40 = 2t
t = 40/2
t = 20 (seconds)
Hence,
it will take 20 seconds for the second skater to catch up (pass)
Alex bought a new truck for $42,935. According to the dealer, the truck will depreciate approximately $4,200 per year. Write and solve a linear equation to find how many years until the car is worth $5,135
Answer:
The truck is worth $5,135 when 9 years have passed
Step-by-step explanation:
Initial value of Alex's new truck: $42,935
Loss of value per year: $4,200
If n years passed, the truck would have lost
[tex]4,200n\ dollars[/tex]
The current value of the truck will be
[tex]V(n)=42,935-4,200n[/tex]
We want to know the value of n at which V is 5,135
[tex]5,135=42,935-4,200n[/tex]
Solving for n
[tex]n=\frac{42,935-5,135}{4,200}[/tex]
n=9 years
The truck will depreciate to a value of $5,135 in approximately 9 years, given a yearly depreciation rate of $4,200.
Explanation:This problem involves finding the duration it will take for the truck to depreciate from $42,935 to $5,135, given it depreciates at a rate of $4,200 per year. The difference in value is $42,935 - $5,135 which equals $37,800. This depreciation amount has to be distributed over the years so we divide it by the yearly depreciation rate. This is represented by the equation 37,800 = 4,200x, with x being the number of years. Thus, solving for x gives x = 37,800 / 4,200 which is approximately 9 years. Therefore, it will take about 9 years for the truck to depreciate to a value of $5,135.
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Rishav takes a loan of rupees 10000 from a bank for a period of 1 year. The rate of interest is 10%
per annum. Find the interest and the amount he has to the pay at the end of a year.
Answer:
The simple interest on the given principal after 1 year = Rs. 1,000
The amount Rishav has to pay after an year = Rs 11,000
Step-by-step explanation:
Here, the Principal amount taken = Rs 10,000
Rate of Interest = 10%
Time Period = 1 year
Now, the SIMPLE INTEREST = [tex]\frac{P \times R \times T}{100}[/tex]
or, [tex]SI = \frac{10,000 \times 10 \times 1}{100} = 1,000[/tex]
So, the simple interest on the given principal after 1 year = Rs. 1,000
Now, Amount = Principal + Simple Interest
or , A = 10,000 + 1,000 = 11, 000
Hence, the amount Rishav has to pay after an year = Rs 11,000